Mixed deterministic and probabilistic networks

. Author manuscript; available in PMC: 2010 Oct 25.

Published in final edited form as: Ann Math Artif Intell. 2008 Nov 1;54(1-3):3–51. doi: 10.1007/s10472-009-9132-y

Procedure Process-bucket-REL_p (⇓, (λ₁, …, λ_j),(R₁, …, R_r))

if bucket_p contains evidence X_p = x_p then

1. Assign X_p = x_p to each λ_i and put each resulting function in the bucket of its latest variable

2. Apply arc-consistency (or any constraint propagation) over the constraints in the bucket.

Put the resulting constraints in the buckets of their latest variable and move any bucket with single domain to top of processing

else

1. Apply directional i-consistency (DIC(i))

2. Generate

λ^{p} = \sum_{{x_{p} ∣ {\bar{x}}_{U_{p}} \in ⋈_{j} R_{j}}} \prod_{i = 1}^{j} λ_{i}

with specialized sparse operations or search-based methods.

Add λ^p to the bucket of the latest variable in U_p, where

U_{p} = \cup_{i = 1}^{j} S_{i} \cup_{i = 1}^{r} Q_{i} - {X_{p}}